The present invention relates generally to reflecting structures and, more particularly, to reducing cyclic error in a beam launcher for an interferometer.
Precision laser interferometry is used to precisely measure the distance between two fiducial points, such as corner cube retro-reflectors (“retros”). An interferometer typically includes three components: (1) a radiation source (e.g., a laser), (2) a beam launcher, and (3) a signal processor (e.g., an observer or a photo-detector and associated electronic circuits). In some configurations, the photo-detector is included in the beam launcher component, while much of the supporting electronics (e.g., the phase meter(s) and computer) remain with the signal processor.
Some existing beam launchers for interferometers do not produce collinear antiparallel beams. Alternatively, if the launchers do produce collinear antiparallel beams, the launchers suffer from problems including thermal drift, cross talk, beam-walk, and/or non-common-path optics, among others.
Some existing launchers that do not produce collinear antiparallel beams sometimes function by directing a single beam towards a first one of the retros. The single beam hits the first retro at a point offset from a vertex of the retro. The retro-reflected beam emerges from the first retro at a symmetrically located offset point, and the beam then is directed to a second retro. The beam and retros are positioned and aligned such the reflected beam hits the second retro also offset from the vertex, with the emerging beam doubly reflected back to an entrance point on the launcher. Such a circuitous configuration is sometimes referred to as a “racetrack” configuration. Any imperfection in the construction of a retro can affect the orientation of the individual facets of the retro, which can cause the retro-reflected beam to emerge at a deflected angle, giving a “dihedral” error that affects the measured distance. If, in addition, the retro or launcher moves in such a manner as to cause a lateral beam displacement, this displacement times the deflection angle results in an error in the measured distance (an example of a “beam-walk” error). Other considerations are size limitations. For instance, the acceptance aperture of the retro has to be at least twice, and often multiple times, the diameter of the measurement laser beam.
An alternative to the racetrack configuration is a “vertex—vertex” configuration, in which beam(s) follow paths described by an ideal line connecting the vertices of the two retros. This can be accomplished by the use of a single beam that leaves the beam launcher, interrogates the first retro, passes back through the beam launcher, interrogates the second retro, and then returns once again to the beam launcher. Alternatively, the beam launcher can emit two distinct beams, each of which interrogates one retro.
An advantage of the vertex—vertex configuration is that the aperture of the retro does not need to be significantly larger than the diameter of the laser beam. Another advantage of this configuration is that by being centered on the vertex, different portions of the beam hit different facets of the retro in different sequences, and the resulting dihedral errors cancel out to some degree. On the other hand, the vertex—vertex configuration may have a greater sensitivity to irregularities of the retros' reflective surfaces near the edges of the facets as compared to the racetrack configuration. The vertex—vertex also lacks the ability to have two independent launchers measure the distance between a given pair of fiducials, as may be required by redundancy considerations.
Precision laser interferometry can be carried out in at least two modes, namely, the “homodyne” mode or the “heterodyne” mode. Either mode can be used for either the racetrack configuration or the vertex—vertex configuration. A vertex—vertex configuration that utilizes two distinct measurement beams requires two complete sets of the elements.
In the homodyne mode, a beam launcher splits a laser beam of a single frequency into two beams. One beam is directed out to the retro(s) to measure the distance. Upon returning to the beam launcher, the beam is aligned and collocated (and the polarization aligned, if needed) with the other portion of the original beam, and the resulting combined beam is directed onto a photo-detector. If the extra distance traveled by the measurement beam is an integer multiple of half the laser wavelength, then, when recombined, the two beams are in phase and add constructively, resulting in an increased signal from the photo-detector. If the measurement beam is an odd multiple of a quarter of the wavelength longer, the beams add destructively, resulting in a reduced signal from the photo-detector. If the distance between the retros changes, the signal fluctuates, and the fluctuations in the signal give a measure of the relative motion of the retros. A signal processor (e.g., an observer or a photo-detector and electronic circuit) “counts fringes” to determine the change in distance between the retros relative to an initial distance. The resolution of a homodyne interferometer is limited, as it is difficult to measure changes in distance significantly smaller than the laser wavelength (typically a half to several micrometers) due to intensity fluctuations of the laser.
A heterodyne interferometer configuration uses two beams that have each been offset in frequency to slightly different frequencies. Typically, the beams originate from a single laser. The difference between the frequencies is chosen to be convenient for detectors and electronics. Typically, the frequency difference is in the range of about 10 kHz to about 100 MHz. Typically, one frequency-offset laser beam (the “measurement beam”) emanates from the beam launcher to interrogate the distance to the retro(s) while the second frequency-offset laser beam (the “local oscillator” or LO) beam remains internal to the beam launcher. When the measurement beam and the LO beam are aligned, collocated, and with aligned polarizations, and are directed onto the photo-detector, the photo-detector produces a “beat” signal. By comparing this beat signal to the known difference of frequency offsets between the laser beams, it is possible to track changes in the relative phase of the signal to find the change in retro distance relative to the initial value. With precision phase meters, it is possible to resolve distances to small fractions of the laser wavelength, resulting in measurements with sub-nanometer precision.
When measuring distances with fine precision, various error sources can affect the results. The laser intensity can fluctuate. The laser radiation is often routed to the beam launcher by means of optical fibers. Small effects, such as a temperature variation or a strain on the fiber, can affect the apparent optical length of the fiber and can result in a phase change that erroneously appears to be a measured displacement of the fiducials. These errors can be reduced by replacing the “known difference” of the laser frequency offsets with a “reference signal” that measures the frequency difference directly. This reference signal is created by mixing a portion of the LO beam with the “reference beam”, which is a portion of the first laser beam that does not interrogate the distance between retros, and directing the combined beam onto a second photo-detector. The use of a reference beam significantly reduces the errors introduced by any common element (e.g., laser or fiber), but it cannot correct for elements that are unique to the measurement path or the reference path. Other errors can be reduced by sharing elements between the measurement and LO beams. The measurements are not affected by elements in the beam-path “downstream” from the point where the two laser beams are first combined (the point where they become aligned, like-polarized, and collocated), as the elements are common to both beams. A beam-launcher in the vertex—vertex configuration with two distinct measurement beams may share a single reference signal or may require two distinct reference signals.
FIG. 1 shows an example of an existing implementation of a vertex—vertex launcher 10 that has a single measurement beam and that utilizes polarization to allow the measurement beam to pass through the beam launcher between retros. This launcher has a first laser measurement beam 12 with “S” polarization and a second laser beam 14 that is orthogonally polarized (“P” polarized). The two beams can share much of the optical path. They do not heterodyne because of the orthogonal polarization. A polarizing beam splitter (PBS) 20 transmits radiation with one polarization (e.g., the “P” polarized beam, which is used as the LO beam) and diverts the other beam (e.g., the “S” polarized beam, used as the measurement beam). The diverted beam goes through a first quarter-wave plate 22 (to change the beam polarization to “circular”), out to one of the retros 24, back through the first quarter-wave plate 22 (the beam now has “S” polarization), through the PBS 20, through a second quarter-wave plate 26 (the beam is now circularly polarized again), out to the second retro 28, back through the second quarter-wave plate 26 (now “P” again), and into the PBS 20 where it is then reflected to again become collocated and aligned with the undiverted beam. The two beams then pass through a polarizer 30 that has its polarization axis oriented midway between “P” and “S” which aligns the polarizations of the two beams. At this point, the two beams combine and heterodyne. The resulting combined beam is directed to a detector 32. Portions of the two beams are picked off prior to the PBS, passed through a second polarizer 36, and directed to a second detector 38 to provide the reference signal. One problem with this approach is that the measurement beam experiences optics (e.g., the two quarter-wave plates) are not common to either the LO or reference beams. This introduces errors that do not cancel out. A second problem with this approach is that the beam polarizations and the PBS are not perfect, resulting in “cross talk”. Such cross talk contaminates the signal, resulting in a phase shift (measurement error) called “cyclic error” that can make the measured distance longer or shorter than the actual distance.
Some other proposed launcher schemes involve having the measurement and reference beams aligned and adjacent but not concentric. When the beams are mixed with the LO beam, they experience a relative phase shift that is the product of the angular misalignment of the LO beam with respect to the other beams and the offset distance between the centroids of the reference and measurement beams. A constant phase offset is not a problem since all measurements are relative to initial values. However, various optical elements, such as a beam-splitter that combines the LO beam with the measurement and reference beams, may vary the angle of the LO beam as a function of temperature (due to both thermal expansion and changes in the index of refraction with temperature). This changed angle times the centroid offset distance may produce an unacceptably large error.
FIG. 2 shows the basic heterodyne interferometer. The heterodyne configuration is desirable because even minor intensity fluctuations in laser power give unacceptably large phase shifts in the alternative homodyne configuration. A laser beam is routed into an optical fiber 50 and then split. Each beam is frequency-shifted by an acousto-optic modulator (“AOM” 52a, 52b), with some convenient offset frequency between them. The laser light is then routed to the beam launcher 54 (within the dotted line) by an optical fiber network.
Inside the launcher 54, the beams exit the fibers and are collimated (for example, by lenses 56a, 56b), and the two beams then are routed by bean-splitters 58a, 58b (half-reflective mirrors). One beam (the Measurement Beam) interrogates the retro 60, and then upon return is mixed with the other beam (the “local oscillator”, or LO beam) to create the heterodyne (beat) signal. This is then detected by a detector 62 and processed, and the resulting signal is compared with the signal that drove the AOMs 52a, 52b. 
A problem with this configuration is that it is not accurate enough for some applications. If the optical fiber were stressed by a slight bend, or if the temperature of an optic were to change slightly, this would cause a phase shift that may be small, but that nonetheless is large compared to picometers. FIG. 3 shows one solution that picks off part of the laser light as a “Reference Beam”. The same reference characters are used for the same components that are common to both FIGS. 2 and 3. Beam “A” passes through all the fiber distribution networks and collimators, and then a part of the laser beam is broken off (via beam splitter 72 and mirror 74) and mixed with the LO beam (“B”) (via beam splitters 76, 78) to recreate the beat signal. The rest of the “A” laser beam is the Measurement Beam that interrogates the retro 60. Each beam is mixed with the LO beam and routed to a detector (62, 82). The resulting signals are compared in the phase meter 84 to give the measurements. This requires about twice as much electronics and optics, but it does measure and compensate for most of the phase errors in the fibers and optics.
Even this is not adequate for some applications. If the path lengths within optics do not match exactly, then even modest changes in temperature can introduce errors. (For example, in the layout in FIG. 3, both beams “A” and “B” pass through two beam-splitter optics before mixing for the measurement channel, but in the reference channel beam “A” goes through an extra piece of glass. Even a milli-Kelvin temperature change could cause a 100 pm error.) Other considerations are that the different optics all have to experience exactly the same temperature (or at least maintain a constant difference), and the relative positions of the optics have to be stable to better than the overall required picometer accuracy.
In short, laser interferometer beam launchers that have non-common, optical paths for the reference and measurement beams suffer from thermal drifts due to even minor thermal gradients. Previous launcher designs with common beam paths have used polarization to separate the measurement and reference channels, but leakage by the polarization elements caused excessive signal contamination that caused excessive cyclic error.